Method and apparatus for performing multiport through-reflect-line calibration and measurement

ABSTRACT

A method of calibrating a measurement path of a vector network analyzer having at least two reference receivers, and a total of 2N measurement ports, where N is an integer comprises the steps of presenting a high reflect calibration standard at each measurement port and measuring a reflection characteristic for each measurement port. The method further comprises the steps of presenting a line calibration standard and a through calibration standard is presented between N direct pairs of the measurement ports and measuring reflection and transmission responses to each standard. From these measurements, the method calculates directivity, source match, and reflection tracking error coefficients for each one of the measurement ports.  
     An apparatus for calibrating a measurement path comprises a VNA having at least two reference receivers, two test channels, and a total of 2N measurement ports, wherein N is an integer. The apparatus further comprises a means for measuring and storing reflection and transmission characteristics for each measurement port when a high reflect, a line, and a through calibration standard is connected thereto. The apparatus further comprises a means for calculating directivity, source match, reflection tracking, load match, forward transmission tracking, and reverse transmission tracking for each one of the measurement ports.

BACKGROUND

[0001] A vector network analyzer (“VNA”) is used to characterize thebehavior of an electrical device over a band of frequencies. Because ofmismatches and leakage, it is not currently possible to directly measurea device under test (“DUT”) at high frequencies without calibration ofthe VNA. Errors exist in any measurement using a VNA. These measurementerrors contribute to the uncertainty of the measurement attributableonly to the DUT. By quantifying these measurement errors, their effectscan be mathematically removed from the measurement to yieldcharacterization parameters for the device itself. As one of ordinaryskill in the art can appreciate, the better the quantification of themeasurement errors, the better the ability to remove their effects onthe device characterization. Measurement errors in the VNA can beseparated into two categories: random errors and systematic errors.Random errors are non-repeatable measurement variations due to noise andtemperature changes. Random errors are unpredictable and are difficultto adequately quantify. Systematic errors are repeatable measurementvariations in the VNA test-set hardware. Systematic errors arepredictable and are possible to quantify and mathematically remove.Systematic errors are the most significant source of VNA measurementuncertainty in the characterization of a device. Therefore, it isbeneficial to quantify and remove the systematic errors from the VNAmeasurements. Conventionally, quantification of the systematic errors isachieved through a VNA calibration. By connecting a number of knowncalibration artifacts to ports of the VNA, one can measure thecalibration artifacts, compare the measured results against knownresults, and then algorithmically extract systematic error coefficientsfrom the contribution made to the measurement from the known calibrationdevice. Measurements of an unknown device, thereafter, use thesystematic error coefficients to mathematically extract thecharacteristics attributable only to the DUT.

[0002] There are a number of calibration procedures available for a2-port VNA. Calibration methods are named after the group of calibrationstandards used to extract systematic error coefficients. Some of themore common methods use short, open, load and through calibrationstandards (“SOLT”), through, reflect, and line calibration standards(“TRL”) and a series of electronic loads used as calibration standards(“electronic calibration” or “Ecal”).

[0003] A preferred method in metrology laboratories is the TRLcalibration. It is preferred because it achieves the most accurateassessment of the systematic errors. This is due to the use of anairline standard that can be manufactured very precisely. Additionally,there is no need to know the magnitude of the reflection coefficient ofthe “reflect” calibration artifact and no need to know the delay of the“line” calibration artifact. Better measurement accuracy in amanufacturing environment provides better feedback in product processcontrol as well as more accurate statistical models for the product costanalysis. Better measurement accuracy in a research and engineeringenvironment provides a more accurate device model permitting simulatorsto more accurately predict behavior of the product in the context of acircuit.

[0004] U.S. patent application Ser. No. 10/098,040 having priority dateSep. 18, 2000 entitled “Method and Apparatus for Linear Characterizationof Multiterminal Single-ended or Balanced Devices” (herein “the '040patent application Ser. No. ”), and other U.S. Patent Applicationsclaiming priority from the same Provisional Application, disclose amethod and apparatus for an SOLT calibration applicable to multiportdevices. With specific reference to FIG. 1 of the drawings, there isshown a system block diagram of a 4-port VNA 100 connected to a deviceunder test 101 (“DUT”) as described by the '040 patent application Ser.No. in which a single reference channel 102 and two test channels, firsttest channel 111 (“A”) and second test channel 112 (“B”), are deployed.The reference channel 102 samples the incident signal, generated bysignal generator 105, through a reference channel sampler 110 placed inseries between the signal generator 105 and source transfer switch 106.The source transfer switch 106 electrically connects the signalgenerator 105 to a first signal path 107 or a second signal path 108.The source transfer switch 106 terminates the signal path 107 or 108that is not connected to the signal generator 105 in a source transfercharacteristic impedance 109. A switching network 150 provides for aconnection of the first or second test channel 111, 112 to one of 2Nmeasurement ports 103 ₁, through 103 _(2N). The switching network 150 istaught in the '040 patent application Ser. No., the teachings of whichare hereby incorporated by reference.

[0005] The first and second test channels 111, 112 measure the scatteredreflected and transmitted signals from one of the measurement ports 103connected to the DUT 101 in response to the stimulus from the signalgenerator 105. The test set-up of FIG. 1 provides for a complete SOLTcalibration methodology. There is a need, however, for a more accuratemethod of device characterization. Under the prior art, the TRLcalibration method provides for improved calibration accuracy, but isapplicable only to 2 port devices. There is a need, therefore, for amethod and apparatus for more accurate calibration and measurement ofmultiport devices.

SUMMARY

[0006] A method of calibrating a measurement path of a vector networkanalyzer comprises the steps of providing a vector network analyzerhaving at least two reference receivers, and a total of 2N measurementports, where N is an integer. A high reflect calibration standard ispresented at each measurement port and the VNA measures a reflectioncharacteristic for each measurement port. A line calibration standard ispresented between N direct pairs of the measurement ports. The VNA thenmeasures forward and reverse reflection and transmission characteristicsfor each one of the N direct pairs. A through calibration standard ispresented between each one of the N direct pairs and forward and reversereflection and transmission characteristics for each one of the N pairsis measured. The method then calculates directivity, source match, andreflection tracking error coefficients for each one of the measurementports.

[0007] An apparatus for calibrating a measurement path of a vectornetwork analyzer (“VNA”) comprises a vector network analyzer having atleast two reference receivers, two test channels, and a total of 2Nmeasurement ports, wherein N is an integer. The system further comprisesa means for measuring and storing high reflect characteristics for eachmeasurement port when a high reflect calibration standard is connectedthereto, line forward and reverse reflection and transmissioncharacteristics for each one of N direct pairs of the measurement portswhen a line calibration standard is connected therebetween, directthrough forward and reverse reflection and transmission characteristicsfor each one of the N direct pairs when a through calibration standardis connected therebetween, and indirect through forward and reversereflection and transmission characteristics for each one of said N−1indirect pairs of said measurement ports when said through calibrationstandard is connected therebetween. The system further comprises a meansfor calculating directivity, source match, and reflection tracking foreach one of the measurement ports based upon the high reflectcharacteristics, said line forward and reverse reflection andtransmission characteristics, and said through forward and reversereflection and transmission characteristics, load match for eachmeasurement port and forward transmission tracking and reversetransmission tracking for each one of the N direct pairs and N−1indirect pairs.

BRIEF DESCRIPTION OF THE DRAWINGS

[0008]FIG. 1 illustrates a prior art test set-up and VNA.

[0009]FIG. 2 shows an apparatus according to the teachings of thepresent invention.

[0010]FIGS. 3 through 16 show steps for measuring direct pairs ofmeasurement ports in an embodiment of a method according to the presentteachings.

[0011]FIGS. 17 and 18 show steps for measuring indirect pairs ofmeasurement ports in an embodiment of a method according to the presentteachings.

[0012]FIG. 19 shows a flow graph of error coefficients for X and Y erroradapters.

[0013]FIGS. 20 and 21 show steps for measuring proximal pairs ofmeasurement ports in an embodiment of a method according to the presentteachings.

[0014]FIGS. 22 through 26 illustrate a flow chart of an embodiment of amethod according to the present teachings.

DETAILED DESCRIPTION OF INVENTION

[0015] With specific reference to FIG. 2 of the drawings, there is showna system block diagram of a 4-port VNA 200 that deploys first and secondreference channels 201, 202, respectively, and first and secondreference channel samplers 110, 210, respectively. In the test set-upshown in FIG. 2, the samplers 110, 210 in a specific example may bebridges or directional couplers. The reference channel samplers 110, 210are placed in the first and second signal paths 107, 108 on an oppositeside of a signal transfer switch 106 from signal generator 105. Thesamplers 110, 210 extract in one direction a small and predictableportion of the signal present on the first and second signal paths 107,108 for measurement by the first and second reference channels 201, 202,respectively. The sampled portion is typically −10 dB to −20 dB relativeto the signal level on the signal path 107 or 108. The source transferswitch 106 connects either the signal generator 105 to the first signalpath 107 and a signal transfer switch terminating load 109 to the secondsignal path 108 or connects the signal generator 105 to the secondsignal path 108 and connects the signal transfer switch terminating load109 to the first signal path 107. In a specific embodiment, there areonly two switch positions for the signal transfer switch 106.

[0016] A system for measuring a multiple port DUT 101 has as manymeasurement ports 103 ₁ through 103 _(2N) as there are DUT ports. Theillustrative example shown in the drawings includes a 4-port DUT 101connected to measurement ports 103 ₁, 103 ₂, 103 ₃, and 103 ₄. Theteachings of the present invention, however, may be applied to amultiport test set-up for measuring DUTs having more than four deviceconnections. A switch network 150 permits connection of each measurementport 103 ₁ through 103 _(2N) to a first or second signal path 107, 108or to a local terminating impedance, 104 ₁ through 104 _(2N). Certainswitch network configurations connect one of the measurement ports 103to the first signal path 107 or/and a different one of the measurementports 103 to the second signal path 108 while the remaining paths areterminated in the local terminating impedance 104. The switch network150 also has sampling arms 113, sampling arms 113 ₁ through 113 ₄ in theillustrated embodiment. The sampling arms 113 ₁ through 113 ₄ eachcomprise a sampler 114 that samples a small and predictable portion ofthe signal level present at the respective measurement port 103. Thesampler 113 may be a coupler or a bridge that takes somewhere between−10 dB and −20 dB of the signal level from the signal level present onthe respective measurement port 103. In a specific embodiment accordingto the present teachings, the portion sampled from the measurement ports103 is substantially the same portion sampled from the signal paths 107,108. The sampled signal may then be connected to either a first orsecond test channel 111, 112 through a respective sampling switch 115 ormay be connected to a sampling arm terminating load 116. A switchnetwork 150 of this configuration may connect a reflection path from themeasurement ports 103 to one of first and second test channels 111, 112while terminating the reflection paths from measurement ports 103 notconnected to a test channel in a local sampling arm terminatingimpedance 116.

[0017] In a method according to the teachings of the present invention,a TRL calibration on a multi-port DUT having 2N device connections isperformed by conducting a conventional 2-port TRL calibration first oneach one of N direct pairs of the measurement ports. A user may definethe N direct pairs by representing all measurement ports 103 ingroupings of two measurement ports 103, where a first port in the directpair is capable of connection to the first test channel 111 and asecond, port in the direct pair is capable of connection to the secondtest channel 112. As an example, if there are 2N measurement ports, thedirect pairs of measurement ports are measurement ports 103 ₁ and 103_(N+1), measurement ports 103 ₂ and 103 _(N+2), et seq. up to the directpair of measurement ports 103 _(N) and 103 _(2N) where measurement ports103 ₁ through 103 _(N) are capable of connection to the first testchannel 111 and measurement ports 103 _(N+1) through 103 _(2N) arecapable of connection to the second test channel 112.

[0018] The method according to the present teachings then performs athrough measurement on N−1 indirect pairs of the measurement ports 103for a 2N port DUT. The N−1 indirect pairs are defined as those groupingsof two measurement ports 103 that are not represented in the set ofdirect pairs of measurement ports where a first measurement port in theindirect pair is capable of connection to the first test channel 111 andthe second measurement port in the indirect pair is capable ofconnection to the second test channel 112. In the illustrated example,there are two direct pairs; first direct pair comprising measurementports 103 ₁ and 103 ₃ and second direct pair comprising measurementports 103 ₂ and 103 ₄. Also in the specific example, there are twoindirect pairs; first indirect pair comprising measurement ports 103 ₁and 103 ₄ and second indirect pair comprising measurement ports 103 ₂and 103 ₃.

[0019] With specific reference to FIG. 3 of the drawings, there is showna high reflect calibration standard 301 (“the reflect 301”) connected tothe measurement port 103 of the first direct pair that is capable ofconnection to the first test channel 111. In the illustrated embodiment,this is measurement port 103 ₁. The switching network 150 is then set sothe measurement port 103 ₁ is connected to the first signal path 107 andthe respective sampling arm 113 ₁ is connected to the first test channel111. All remaining unused measurement ports 103 ₂, 103 ₃ and 103 ₄ areterminated in their respective local terminating loads 104 and theirrespective sampling arms 113 are connected to the sampling armterminating loads 116 ₂, 116 ₃, and 116 ₄. As one of ordinary skill inthe art appreciates, for measurement of the measurement port 103 ₁ onlythe switch network configuration that terminates in a characteristicimpedance those measurement ports 103 that are capable of connection tothe first test channel 111 are important to the results. Because theisolation of the switches that comprise the switch network 150 is sohigh, the measurement ports 103 capable of connection to the second testchannel 112 do not figure in the high reflect measurement. The reflect301 may have an unknown magnitude, but its phase charcateristics must beknown. The signal generator 105 is then swept through a desiredfrequency range as programmed by an operator and measurements are takenat specific frequencies across the range. During the frequency sweep theVNA 200 measures and stores a ratio of the measured signal level at thefirst test channel 111 over the measured signal level at the firstreference receiver 201. The resulting ratio is a frequency dependantreflection coefficient, herein referred to as a high reflectcharacteristic for measurement port 103 ₁.

A_(reflect) _(—) ₁/R1_(reflect) _(—) ₁

[0020] With specific reference to FIG. 4 of the drawings, the samereflect 301 is disconnected from measurement port 103 ₁ and is connectedto the remaining measurement port in the first direct pair, measurementport 103 ₃ in the specific example. The switch network 150 is thenconfigured so that the measurement port 103 ₃ is in the second signalpath 108, the first signal path 107 is terminated in a characteristicimpedance 109, and the sampling arm 113 ₃ is connected to the secondtest port 112. The unused measurement ports 103 capable of connection tothe second test port 112, the measurement port 103 ₄ in the specificexample, are terminated in the local characteristic impedance 104 in theswitching network 150. The sampling arms 113 of the unused measurementports 103 are also terminated in the respective sampling arm terminatingloads 116. The signal generator 105 stimulates the second signal path108 with a signal that is swept over the same desired frequency range asin the reflection measurement of measurement port 103 ₁. The VNA 200measures and stores a measurement of a ratio of the measured signallevel at the second test channel 112 over measured signal level of thesecond signal path 108 as presented to the second reference receiver 202yielding a frequency dependent array of reflected signal level, hereinreferred to as a high reflect characteristic for measurement port 103 ₃:

B_(reflect) _(—) ₃/R2_(reflect) _(—) ₃

[0021] With specific reference to FIG. 5 of the drawings, a next step inthe calibration process is to connect a low-loss delay line calibrationstandard 401 (“the line 401”) between the first direct pair, measurementport 103 ₁ and measurement port 103 ₃ in the illustrated example. In apreferred embodiment, the line 401 is an airline i.e. a delay linehaving an air dielectric, which is commonly used in metrologylaboratories. For on-wafer measurements, a delay line is used. The delayof the line 401 is unknown, but the physical dimensions of the line 401relate to a range of calibration frequencies. Additional delay linecalibration standards can be used to cover a broader frequency range asdesired. The delay of the line 401 is defined over a range offrequencies bounded by approximately more than 20 degrees phase shift ata lowest specified frequency and less than 160 degrees phase shift at ahighest specified frequency. At frequencies around 500 MHz and below,coaxial airline dimensions become very large and not practical. In thiscase, and with specific reference to FIG. 6, two high-quality matchedloads 501 (“the matched loads 501”) are connected to each measurementport 103 of the direct pair. The matched loads 501 are used forcalibrating the VNA in a frequency range down to the lowest VNAfrequency. The resulting calibration values of the line 401 and thematched loads 501 are different, but the algorithmic formulations usingthe measured ratios are the same.

[0022] With specific reference to FIG. 5 of the drawings in which theline 401 is measured, the transfer switch 106 is set so that the signalgenerator 105 stimulates the first signal path 107 and the second signalpath 108 is terminated at the characteristic impedance 109. The switchnetwork 150 is configured so that the measurement port 103 ₁ accepts thestimulus signal from the first signal path 107 and the signal from thesampling arm 113 ₁ is presented to the first test port 111. The switchnetwork 150 is further configured so that the measurement port 103 ₃ isterminated in the transfer switch characteristic impedance 109 throughsecond signal path 108 and a transmitted signal is presented to thesecond test port 112 through sampling arm 113 ₃. The signal generator105 sweeps the desired frequency range and the VNA 200 measures signallevel from the first and second test channels 111, 112 and the first andsecond reference receivers 201, 202 and stores the results in a dataarray. For purposes of clarity and consistency only, when the signalgenerator 105 is connected to the first signal path 107, all resultingmeasurements are considered forward direction measurements. Accordingly,the measurements made of the line 401 in the forward direction arerepresented as the data arrays:

[0023] A_(f) _(—) _(line) _(—) ₁₃,

[0024] B_(f) _(—) _(line) _(—) ₁₃,

[0025] R1_(f) _(—) _(line) _(—) ₁₃, and

[0026] R2_(f) _(—) _(line) _(—) ₁₃.

[0027] where each array comprises a series of measured points atspecific frequencies along the desired frequency range.

[0028] The transfer switch 106 is then reconfigured (not shown in thedrawings) so that the signal generator 105 stimulates the second signalpath 108 and the first signal path 107 is terminated in the transferswitch characteristic impedance 109. The configuration of the switchnetwork 150 is not changed from the forward direction measurements. Thesignal generator 105 again sweeps the desired frequency range and theVNA 200 measures signal level from the first and second test channels111, 112 and the first and second reference receivers 201,202 and storesthem in data arrays. For purposes of clarity and consistency only, whenthe signal generator 105 is connected to the second signal path 108, allresulting measurements are considered reverse direction measurements.Accordingly, the measurements made of the line 401 in the reversedirection are represented as the data arrays:

[0029] A_(r) _(—) _(line) _(—) ₁₃,

[0030] B_(r) _(—) _(line) _(—) ₁₃,

[0031] R1_(r) _(—) _(line) _(—) ₁₃, and

[0032] R2_(r) _(—) _(line) _(—) ₁₃.

[0033] where each array comprises a series of measured points atspecific frequencies along the desired frequency range.

[0034] If a broader frequency range is necessary, the same measurementprocedure is performed on the first direct pair, measurement ports 103 ₁and 103 ₃ in the specific embodiment, with a different airline coveringa different frequency band. In addition, the matched loads 501 as shownin FIG. 6 of the drawings may be used to simulate a high loss linehaving a perfect match in order to take measurements at lowerfrequencies than are practical with an airline calibration standard.Depending upon the matched load, the quality of the match at higherfrequencies, and the desired frequency range, the matched loads may beused in place of the airline calibration standard. As new measurementsare made for the different frequency ranges using the appropriatecalibration standards, the results are stored in the forward and reversedirection arrays with each data point corresponding to a specificstimulus signal frequency. Accordingly, the calibration frequency bandcan extend over more frequencies than is possible with a single airlinecalibration standard.

[0035] With specific reference to FIG. 7 of the drawings, a next step inthe calibration process is to connect a through calibration standard 601(“the thru 601”) between the first direct pair, measurement port 103 ₁and measurement port 103 ₃ in the illustrated embodiment. The thru 601may have either a zero length or a non-zero length. In either case, anelectrical length of the thru 601 must be a known value. For on-wafermeasurements, it is not possible to obtain a high quality zero thrucalibration standard. Accordingly, for on-wafer measurements, thenon-zero thru calibration standard is used.

[0036] To measure the thru 601, the transfer switch 106 is set so thatthe signal generator 105 stimulates the first signal path 107 and thesecond signal path 108 is terminated in the transfer switchcharacteristic impedance 109. The switch network 150 is configured sothat the measurement port 103 ₁ accepts the stimulus signal from thefirst signal path 107 and the sampling arm 113 ₁ is connected to thefirst test port 111. The switch network 150 is further configured sothat the measurement port 103 ₃ is terminated in the transfer switchcharacteristic impedance 109 through second signal path 108 and thesampling arm 113 ₃ is connected to the second test port 112. The unusedmeasurement ports 103, which in the specific embodiment comprisemeasurement ports of the second direct pair, measurement port 103 ₂ andmeasurement port 103 ₄, are terminated in the local characteristicimpedances 104 ₂ and 104 ₄, respectively. The sampling arms 113 ₂ and113 ₄ are also terminated in local sampling arm terminating loads 116 ₂and 116 ₄. The signal generator 105 sweeps the desired frequency rangeand the VNA 200 measures signal level from the first and second testchannels 111, 112 and the first and second reference receivers 201, 202and stores the results in memory. According to the nomenclature used forpurposes of the present disclosure, because the signal generator 105 isconnected to the first signal path 107, the resulting measurements areconsidered forward direction measurements. Accordingly, the measurementsmade of the thru 601 in the forward direction are represented as thearrays:

[0037] A_(f13) _(—) _(thru),

[0038] B_(f13) _(—) _(thru),

[0039] R1_(f13) _(—) _(thru), and

[0040] R2_(f13) _(—) _(thru).

[0041] where each array comprises a series of measured points atspecific frequencies along the desired frequency range.

[0042] The transfer switch 106 is then set (not shown) so that thesignal generator 105 stimulates the second signal path 108 and the firstsignal path is terminated in the transfer switch characteristicimpedance 109. The switch network 150 is not changed. The signalgenerator 105 again sweeps the desired frequency range and the VNA 200measures signal level from the first and second test channels 111, 112and the first and second reference receivers 201, 202 and stores them inmemory. Because the signal generator 105 is connected to the secondsignal path 108, the resulting measurements are considered reversedirection measurements. Accordingly, the measurements made of the thru601 in the reverse direction are represented as the arrays:

[0043] A_(r13) _(—) _(thru),

[0044] B_(r13) _(—) _(thru),

[0045] R1_(r13) _(—) _(thru), and

[0046] R2_(r13) _(—thru) .

[0047] where each array comprises a series of measured points atspecific frequencies along the desired frequency range.

[0048] With specific reference to FIG. 8 of the drawings and with thethru 601 still connected, the transfer switch 106 is configured so thatthe signal generator 105 is in the first signal path 107 and the secondsignal path 108 is terminated in the characteristic impedance 109.Measurements of the first direct pair are still being made. Accordingly,the switch network 150 is configured so that the measurement port 103 ₁is connected to the first signal path 107 and the respective samplingarm 113 ₁ is connected to the first test channel 111. The remainingunused measurement ports 103 capable of connection to the first testchannel 111, measurement port 103 ₂ in the specific example, areterminated at respective local characteristic impedances 104, localcharacteristic impedance 104 ₂ in the specific example. In addition, thesampling arm 113 ₂ of the unused measurement port 103 ₂ is terminated inlocal sampling arm characteristic impedance 116 ₂. The switch network150 is further configured so that the measurement port capable ofconnection to the second test channel 112 in the first direct pair,specifically measurement port 103 ₃, is terminated at the respectivelocal characteristic impedance, 104 ₃ in the specific example, and therespective sampling arm, 113 ₃ is connected to the second test channel112. The measurement ports 103 of the direct pairs not being measuredare also terminated in local characteristic impedances, localcharacteristic impedance 104 ₂ and 104 ₄ in the specific example, andthe respective sampling arms 113 ₂ and 113 ₄ are terminated in localsampling arm terminating load 116 ₂ and 116 ₄. The signal generator 105is again swept through the desired frequency range and for eachfrequency point in the range, the VNA 200 measures a ratio of thereflection response over the stimulus and a ratio of the transmissionresponse over the stimulus of the terminated thru 601 and stores thedata in the following arrays:

[0049] A_(f13) _(—) _(termthru)/R1_(f13) _(—) _(termthru)

[0050] B_(f13) _(—) _(termthru)/R1_(f13) _(—) _(termthru).

[0051] With specific reference to FIG. 9 of the drawings, the thru 601is still connected between the measurement ports 103 of the first directpair and the transfer switch 106 is then re-configured so that thesignal generator 105 is in the second signal path 108 and the firstsignal path 107 is terminated in the characteristic impedance 109. Theswitch network 150 is also reconfigured so that the measurement port 103in the first direct pair that is capable of connection to the secondtest channel 112, measurement port 103 ₃ in the illustrated example, isconnected to the second signal path 108 and the respective sampling arm113 ₃ is connected to the second test channel 112. The measurement port103 in the first direct pair that is capable of connection to the firsttest channel 111, measurement port 103 ₁ in the illustrated example, isterminated in the respective local characteristic impedance 104 ₁ andthe respective sampling arm 113 ₁ is connected to the first test channel111. The measurement ports 103 of the direct pairs not being measuredare locally terminated in their characteristic impedances, 104 ₂ and 104₄ in the illustrated example. Additionally, the sampling arms 113 of theunused measurement ports 103, sampling arms 113 ₂ and 113 ₄ in theillustrated example, are terminated in their respective local samplingarm terminating loads 116 ₂ and 116 ₄. The signal generator 105 is sweptthrough the desired frequency range and for each frequency point in therange, the VNA 200 measures a ratio of the signal level of thereflection response of the terminated thru 601 over the signal level ofthe stimulus signal as measured at the reference channel 201, and aratio of the signal level of the transmission response of the terminatedthru 601 over the signal level of the stimulus signal. The measuredvalues are stored in data arrays:

[0052] A_(r13) _(—) _(termthru)/R1_(r13) _(—) _(termthru), and

[0053] B_(r13) _(—) _(termthru)/R2_(r13) _(—) _(termthru).

[0054] With specific reference to FIGS. 10 through 16 of the drawings,the same calibration steps and measurements described in reference toFIGS. 3 through 9 of the drawings, are carried out for the measurementports that comprise the second direct pair, measurement port 103 ₂ andmeasurement port 103 ₄ in the illustrated example. Accordingly, theresulting data gathered through the process for the second direct pairis measured and stored in the data arrays:

[0055] A_(reflect) _(—) ₂,

[0056] R1_(reflect) _(—) ₂,

[0057] B_(reflect) _(—) ₄,

[0058] R2_(reflect) _(—) ₄,

[0059] A_(f24) _(—) _(line),

[0060] B_(f24) _(—) _(line),

[0061] R1_(f24) _(—) _(line),

[0062] R2_(f24) _(—) _(line),

[0063] A_(r24) _(—) _(line),

[0064] B_(r24) _(—) _(line),

[0065] R1_(r24) _(—) _(line),

[0066] R2_(r24) _(—) _(line),

[0067] A_(f24) _(—) _(thru),

[0068] B_(f24) _(—) _(thru),

[0069] R1_(f 24) _(—) _(thru),

[0070] R2_(f24) _(—) _(thru),

[0071] A_(r24) _(—) _(thru),

[0072] B_(r24) _(—) _(thru),

[0073] R1_(r24) _(—) _(thru),

[0074] R2_(r24) _(—) _(thru),

[0075] A_(f24) _(—) _(termthru)/R1_(f24) _(—) _(termthru),

[0076] B_(f24) _(—) _(termthru)/R1_(f24) _(—) _(termthru),

[0077] B_(r24) _(—) _(termthru)/R2_(r24) _(—) _(termthru),

[0078] A_(r24) _(—) _(termthru)/R2_(r24) _(—) _(termthru).

[0079] where all of the data arrays having a single point of measurementfor each frequency measured in the desired frequency range. It is bestpractice to measure the same frequency points along the range so thateach array has a measured value for each frequency point. It isacceptable, however, to interpolate the data to obtain a value for aspecific frequency value as long as the frequency value is within theboundary of the lowest measured frequency and the highest measuredfrequency in the desired frequency range and the interval betweenmeasured frequencies is small enough to fully characterize the DUTincluding any resonances thereof. If multiple line calibration standardsare used to obtain a broader frequency range, the measurements taken bythe VNA 200 are stored in appropriate array elements in a larger arrayhaving an element for each frequency along the frequency range ofinterest. Accordingly, multiple steps of connecting calibrationstandards and making measurements may be performed to completelypopulate a single data array.

[0080] In a multiport calibration according to an aspect of anembodiment of the present invention, the same calibration steps andmeasurements described in FIGS. 3 through 9 of the drawings are carriedout for the measurement ports of all of the direct pairs. The generaldescription of a set of direct pairs for a DUT having 2N ports comprisesthe set where m is a set of integers between 1 and N, and the directpairs are the measurement port 103 _(m) and measurement port 103 _(N+m).Measurements of each direct pair yield a 22 data arrays that are storedand maintained in an embodiment of a system according to the teachingsof the present invention.

[0081] With specific reference to FIG. 17 of the drawings, the next stepof the process is to connect the thru 601 between the first indirectpair of measurement ports, which in the illustrated embodiment comprisesmeasurement port 103 ₁ and measurement port 103 ₄. The signal transferswitch 106 is configured so that the signal generator 105 stimulates thefirst signal path 107 and the second signal path 108 is terminated inthe characteristic impedance 109. The switch network 150 is configuredso that the measurement port 103 of the first indirect pair that iscapable of connection to the first test channel 111, measurement port103 ₁ in the illustrated example, is connected to the first signal path107 and the respective sampling arm 113 ₁ is connected to the first testchannel 111. The switch network 150 is further configured so that themeasurement port 103 of the first indirect pair that is capable ofconnection to the second test channel 112, measurement port 103 ₄ in theillustrated example, is terminated at the respective local terminatingload 104 ₄ and the respective sampling arm 113 ₄ is connected to thesecond test channel 112. All unused measurement ports, measurement port103 ₂ and measurement port 103 ₃ in the specific example, are terminatedin the respective local terminating load 104 ₂ and 104 ₃ and theirrespective sampling arms 113 ₂ and 113 ₄ are terminated in respectivelocal sampling arm terminating loads 116 ₂ and 116 ₃. The signalgenerator 105 is then swept over the desired frequency range and theratio of the signal level at the first test channel 111 over the signallevel at the first reference receiver 201 is measured and stored asadditional data arrays:

[0082] A_(f14) _(—) _(thruterm)/R1_(f14) _(—) _(thruterm), and

[0083] B_(f14) _(—) _(thruterm)/R1_(f14) _(—) _(thruterm).

[0084] The transfer switch 106 is then reconfigured (not shown) so thatthe signal generator 105 stimulates the second signal path 108 and thefirst signal path 107 is terminated in the characteristic impedance 109.The switch network 150 is configured so that the measurement port in thefirst indirect pair that is capable of connection to the first testchannel 111, measurement port 103 ₁, is terminated in the localterminating load 104 ₁. The measurement port in the first indirect pairthat is capable of connection to the second test channel 112,measurement port 103 ₄ in the illustrated example, is connected to thesecond signal path 108. The signal generator 105 is then swept over thedesired frequency range and the ratio of the signal level at the secondtest channel 112 over the signal level at the second reference receiver202 is measured and stored as a additional arrays:

[0085] A_(r14) _(—) _(thruterm)/R2_(r14) _(—) _(thruterm),

[0086] B_(r14) _(—) _(thruterm)/R2_(r14) _(—) _(thruterm).

[0087] Similarly, and with specific reference to FIG. 18 of thedrawings, the same measurement and storage steps made for the firstindirect pair, measurement port 103 ₁ and measurement port 103 ₄ in theillustrated example, are performed for the second indirect pair,measurement port 103 ₂ and measurement port 103 ₃ in the illustratedexample. Briefly, the thru 601 is connected between the measurementports 103 of the second indirect pair. In a first step, the thru 601 isterminated in a local terminating impedance at 104 ₃, is stimulated in aforward direction, while the ratio of the signal level present at thefirst test channel 111 over the first reference receiver 201 is measuredand stored and the ratio of the signal level present at the second testchannel 112 over the first reference receiver 201 is measured and storedto yield the frequency dependent data arrays:

[0088] A_(f23) _(—) _(thruterm)/R1_(f23) _(—) _(thru) _(—) _(term), and

[0089] B_(f23) _(—) _(thruterm)/R1_(f23) _(—) _(thruterm).

[0090] The switch network 150 is then reconfigured so that the signalgenerator 105 stimulates the second signal path 108, the measurementport 103 of the indirect pair capable of connection to the second testchannel 112 is connected to the second signal path 108 and themeasurement port 103 of the indirect pair capable of connection to thefirst test channel 111 is terminated in a local terminating load 104.The signal generator 105 is swept over the desired frequency range andthe ratios are measured and stored to yield the frequency dependentarrays:

[0091] A_(r23) _(—) _(thruterm)/R2_(r23) _(—) _(thruterm), and

[0092] B_(r23) _(—) _(thruterm)/R2_(r23) _(—) _(thruterm).

[0093] In a multiport embodiment of a method according to the teachingsof the present invention, additional similar measurements are taken foreach direct pair and each indirect pair of the measurement ports 103.

[0094] With specific reference to FIG. 19 of the drawings, there isshown a TRL calibration flow graph between any first port and any secondport of the VNA 200. A multiport embodiment has a different calibrationflow graph to represent the directivity 1901, source match 1902, andreflection tracking error coefficients 1903 for the X error adapter 1910and directivity 1904 source match 1905, and reflection tracking errorcoefficients 1906 for the Y error adapter 1920 An embodiment of a methodaccording to the present teachings determines the X error adapter 1910and the Y-error adapter 1920 for each direct pair. The flow graphrepresents an S-parameter matrix for the X error adapter 1910, S_(x),which corresponds to the error artifacts for a first measurement port103 in the direct pair, and an S-parameter matrix for the Y erroradapter 1920, S_(y), which corresponds to the error artifacts for asecond measurements port 103 in the direct pair.

[0095] S-parameter matrix S_(act) represents the S-parameters of anactual calibration standard without the contribution of the X and Yerror adapters. The S-parameter matrices of the X error adapter may beexpressed as T-parameters using the following known conversion whereport 1 is on the left and port 2 is on the right when looking at the DUT101: $\begin{matrix}{{Tx} = {\begin{bmatrix}{Tx}_{11} & {Tx}_{12} \\{Tx}_{21} & {Tx}_{22}\end{bmatrix} = \begin{bmatrix}\frac{1}{{Sx}_{21}} & \frac{- {Sx}_{22}}{{Sx}_{21}} \\\frac{{Sx}_{11}}{{Sx}_{21}} & \frac{{{Sx}_{12}{Sx}_{21}} - {{Sx}_{11}{Sx}_{22}}}{{Sx}_{21}}\end{bmatrix}}} & (1)\end{matrix}$

[0096] Accordingly, the matrix Sx may be converted into correspondingT-parameters expressed as Tx. If the matrix T_(act) _(—) _(thru)expresses the T-parameters of just the thru 601 and T_(meas) _(—)_(thru) expresses the T-parameters of the thru 601 as measured incontext with the X and Y error adapters, then the following relationshipholds true:

T _(x) T _(act) _(—) _(thru) T _(y) =T _(meas) _(—) _(thru)   (2)

[0097] Similarly, if the matrix T_(act) _(—) _(line) expresses theT-parameters of just the line 401 and T_(meas) _(—) _(line) expressesthe T-parameters of the line 401 as measured in context with the X and Yerror adapters, then the following relationship holds true:

T _(x) T _(act) _(—) lineT _(y) =T _(meas) _(—) _(line)   (3)

[0098] If the following relationships are defined:

T _(act x) =T _(act) _(—) _(line) T _(act) _(—) _(thru) ⁻¹   (4)

[0099] and

T _(meas) _(—) _(x) =T _(meas) _(—) _(line) T _(meas) _(—) _(thru) ⁻¹  (5)

[0100] then the following equation can be written

T _(x) T _(act) _(—) _(x) =T _(meas) _(—) _(x) T _(x)   (6)

[0101] The thru 601 and the line 401 are each assumed to be perfectlymatched. Therefore, the value of their reflection coefficient in therespective actual S-parameter matrix is set to zero. If the thru 601 hasa non-zero length transmission coefficient, it is defined by S₂₁ _(—)_(thru)=S₁₂ _(—) _(thru). The line 401 has a transmission coefficientdefined by S₂₁ _(—) _(line) _(—) _(S) ₁₂ _(—) _(line). From equation(4), therefore T_(act) _(—) _(x) may be expressed as: $\begin{matrix}{T_{act\_ x} = \begin{bmatrix}\frac{S_{21{\_ thru}}}{S_{21{\_ line}}} & 0 \\0 & \frac{S_{21{\_ line}}}{S_{21{\_ thru}}}\end{bmatrix}} & (7)\end{matrix}$

[0102] Measurements of the unterminated thru 601 and the line 401, eachprovide eight frequency dependent arrays of measured and stored results.There are four thru forward reflection and transmission arrays and fourthru reverse reflection and transmission arrays. The arrays of measureddata for the thru 601 are used in an algorithmic formulation in theS-parameter domain to compensate for the presence of the signal transferswitch 106 prior to calculation of the T_(meas) _(—) _(x) matrix. Boththe S_(meas) _(—) _(line) and S_(meas) _(—) _(thru) are corrected by theformulation given by: $\begin{matrix}{S_{corrected} = \left\lbrack {\begin{pmatrix}\frac{\frac{A_{f}}{{R1}_{f}} - {\frac{A_{r}}{{R2}_{r}}\frac{{R2}_{f}}{{R1}_{f}}}}{1 - {\frac{{R2}_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}} \\\frac{\frac{B_{f}}{{R1}_{f}} - {\frac{B_{r}}{{R2}_{r}}\frac{{R2}_{f}}{{R1}_{f}}}}{1 - {\frac{{R2}_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}}\end{pmatrix}\begin{pmatrix}\frac{\frac{A_{r}}{{R2}_{r}} - {\frac{A_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}}{1 - {\frac{{R2}_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}} \\\frac{\frac{B_{r}}{{R2}_{r}} - {\frac{B_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}}{1 - {\frac{{R2}_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}}\end{pmatrix}} \right\rbrack} & (8)\end{matrix}$

[0103] where A_(f), B_(f), R1_(f) and R2_(f) are the forward directionraw measurement data, i.e. when the signal transfer switch 106 isdirecting the signal generator 105 to the first signal path 107, andA_(r), B_(r), R1_(r) and R2_(r) are the reverse direction rawmeasurement data, i.e. when the signal transfer switch 106 is directingthe signal generator 105 to second signal path 108.

[0104] Referring now to the measurements of the first direct pair,meaurement ports 103 ₁ and 103 ₃, a corrected S-parameter matrix of thethru 601 measured in cascaded combination with the X and Y erroradapters for the first direct pair is expressed herein as S_(meas13)_(—) _(thru) _(—) _(corrected). The correction formulation shown inequation (8) uses the arrays; A_(f13) _(—) _(thru), B_(f13) _(—)_(thru), R1_(f13) _(—) _(thru), R2_(f13) _(—) _(thru), A_(r13) _(—)_(thru), B_(r13) _(—) _(thru), R1_(r13) _(—) _(thru), and R2_(r13) _(—)_(thru) to calculate S_(meas13) _(—) _(thru) _(—) _(corrected).Converting the S_(meas13) _(—) _(thru) _(—) _(corrected) matrix to thecorresponding T-parameters using equation (1) yields matrix T_(meas13)_(—) _(thru) _(—) _(corrected). To obtain the S_(meas13) _(—) _(line)_(—) _(corrected) matrix for the first direct pair, the correctionformulation shown in equation (8) uses the arrays; A_(f13) _(—) _(line),B_(f13) _(—) _(line), R1_(f13) _(—) _(line), R2_(f13) _(—) _(line),A_(r13) _(—) _(line), B_(r13) _(—) _(line), R1_(r13) _(—) _(line), andR2_(r13) _(—) _(line). Converting the corrected S_(meas13) _(—) _(line)_(—) _(corrected) matrix to the corresponding T-parameters, yieldsmatrix T_(meas13) _(—) _(line) _(—) _(corrected). The T_(meas13) _(—)_(thru) _(—) _(corrected) and T_(meas13) _(—) _(line) _(—) _(corrected)matrices are used in equations (4) and (5) to calculate T_(act) _(—)_(x) and T_(meas) _(—) _(x).

[0105] Referring now to the general case, T_(x) is the T-parametermatrix for the X error adapter and is defined by its matrix elements as:$\begin{matrix}{{Tx} = \begin{bmatrix}{Tx}_{11} & {Tx}_{12} \\{Tx}_{21} & {Tx}_{22}\end{bmatrix}} & (9)\end{matrix}$

[0106] T_(meas) _(—) _(x) is also defined by its matrix elements, and isrepresented as: $\begin{matrix}{T_{meas\_ x} = \begin{bmatrix}T_{meas\_ x11} & T_{meas\_ x12} \\T_{meas\_ x21} & T_{meas\_ x22}\end{bmatrix}} & (10)\end{matrix}$

[0107] From equation (5), T_(meas) _(—) _(x) for measurement ports 103 ₁and 103 ₃, which is expressed as T_(meas13) _(—) _(x), is calculatedusing the T_(meas13) _(—) _(thru) _(—) _(corrected) and T_(meas13) _(—)_(line) _(—) _(corrected) matrices. Accordingly:

T _(meas13) _(—) _(x) =T _(meas13) _(—) _(line) _(—) _(corrected) T_(meas13) _(—) _(thru) _(—) _(corrected) ⁻¹

[0108] Using the relationship in equations (4), substituting the termsin equation (6), and eliminating the S₂₁ _(—) _(thru)/S₂₁ _(—) _(line)term, the following general equation can be written: $\begin{matrix}{\frac{{Tx}_{21}}{{Tx}_{11}} = \frac{\left( {{- T_{meas\_ x11}} + \sqrt{{4T_{meas\_ x12}T_{meas\_ x21}} + \left( {T_{meas\_ x11} - T_{meas\_ x22}} \right)^{2}} + T_{meas\_ x22}} \right)}{2T_{meas\_ x12}}} & (11)\end{matrix}$

[0109] and $\begin{matrix}{\frac{{Tx}_{22}}{{Tx}_{12}} = \frac{\left( {{- T_{meas\_ x11}} + \sqrt{{4T_{meas\_ x12}T_{meas\_ x21}} + \left( {T_{meas\_ x11} - T_{meas\_ x22}} \right)^{2}} + T_{meas\_ x22}} \right)}{2T_{meas\_ x12}}} & (12)\end{matrix}$

[0110] Based upon the T-parameter to S-parameter conversion, Tx₂₁/Tx₁₁and Tx₂₂/Tx₁₂ in terms of the corresponding S-parameter error adaptermatrix may also be expressed as: $\begin{matrix}{\frac{{Tx}_{21}}{{Tx}_{11}} = {{Sx}_{11} = B}} & (13)\end{matrix}$

[0111] and $\begin{matrix}{\frac{{Tx}_{22}}{{Tx}_{12}} = {{{Sx}_{11} - \frac{{Sx}_{12}{Sx}_{21}}{{Sx}_{22}}} = A}} & (14)\end{matrix}$

[0112] As one of ordinary skill in the art can appreciate, equations(11) and (12) are equal. Because there is a square root in the solution,there are two possible mathematical solutions. The smaller valuedsolution, defined by B, corresponds to the directivity error coefficient1901 of error adapter X. The larger valued solution, defined by A, is amathematical combination of source match 1902 and reflection tracking1903.

[0113] As mentioned before, at frequencies around 500 MHz and below, thedimensions of the line 401 become very large and not practical.Calculation of the directivity 1901 and the solution represented by Afor the lower frequencies uses the measurements taken of the twohigh-quality matched loads 501 instead of the line 601. It is assumedthat the matched loads 501 are perfectly matched to the measurement portand have a zero reflection coefficient. The same algorithmicformulations shown in equations (5) through (14) are used. To understandthe usage of the measurement results from the two matched loads, notethat the thru 601 has a non-zero-length transmission coefficient definedby S_(12thru)=S_(12thru). The matched loads 501 have a transmissionisolation coefficient defined by S_(21load)=S_(12load). Due to the highisolation between the matched loads 501, S_(21load) is close to a zerovalue. Accordingly, S21load is set to a very small, non-zero value, suchas 10⁻¹⁰ in order to avoid division by zero ambiguity in the S-parameterto T-parameter conversion. From this, T_(act) _(—) _(x) at the lowerfrequencies can be calculated and is given by: $\begin{matrix}{T_{act\_ x} = \begin{bmatrix}\frac{S_{21{\_ thru}}}{10^{- 10}} & 0 \\0 & \frac{10^{- 10}}{S_{21{\_ thru}}}\end{bmatrix}} & (15)\end{matrix}$

[0114] As shown before, by using equations (4) and (5), substitutingresults into equation (6) and eliminating the S₂₁ _(—) _(thru)/10⁻¹⁰term, equations (11) and (12) are derived. The S-parameters from thematched loads 501 are corrected using equation (8) to yield S_(meas13)_(—) _(load) _(—) _(corrected), which is then converted using equation(1) to yield T_(meas13) _(—) _(load) _(—) _(corrected). The T_(meas13)_(—) _(load) _(—) _(corrected) term is used to calculate T_(meas13) _(—)_(x) in place of the terms measuring the line 401. The calculations inequations (11) and (12), therefore, are the same as for the line 401.

[0115] A similar process is performed to calculate terms in the erroradapter Y. Beginning with equations (2) and (3) and defining thefollowing relationships:

T _(act) _(—) _(y) =T _(act) _(—) _(thru) ⁻¹ T _(act) _(—) _(line)  (16)

[0116] and

T _(meas) _(—) _(y) =T _(meas) _(—) _(thru) ⁻¹ T _(meas) _(—) _(line)  (17)

[0117] then the following equation can be written:

T _(act) _(—) _(y) T _(y) =T _(y)T_(meas) _(—) _(y)   (18)

[0118] With specific reference to FIG. 19 of the drawings, the knownconversion for T-parameter matrix for the error adapter Y in terms ofthe S-parameters where port 1 is on the right and port 2 is on the leftwhen looking at the DUT 101 is: $\begin{matrix}{{Ty} = {\begin{bmatrix}{Ty}_{11} & {Tx}_{12} \\{Ty}_{21} & {Ty}_{22}\end{bmatrix} = \begin{bmatrix}\frac{1}{{Sy}_{12}} & \frac{- {Sy}_{11}}{{Sy}_{12}} \\\frac{{Sy}_{22}}{{Sy}_{12}} & \frac{{{Sy}_{12}{Sy}_{21}} - {{Sy}_{11}{Sy}_{22}}}{{Sy}_{12}}\end{bmatrix}}} & (19)\end{matrix}$

[0119] Accordingly, the matrix Sy may be converted into correspondingT-parameters expressed as Ty. The T_(meas13) _(—) _(thru) _(—)_(corrected) and T_(meas13) _(—) _(line) _(—) _(corrected) matrices havealready been calculated and are used in equation (17) to calculateT_(meas13) _(—) _(y), where: $\begin{matrix}{T_{meas13\_ y} = \begin{bmatrix}T_{meas13\_ y11} & T_{meas13\_ y12} \\T_{meas13\_ y21} & T_{meas13\_ y22}\end{bmatrix}} & (20)\end{matrix}$

[0120] Using equation (18), substituting the relationships in equations(16) and (17) and eliminating the S_(21thru)/S_(21line) term, thefollowing equation for the first direct pair can be written:$\begin{matrix}{\frac{{Ty}_{12}}{{Ty}_{11}} = \frac{\left( {{- T_{meas13\_ y11}} + \sqrt{{4T_{meas13\_ y12}T_{meas13\_ y21}} + \left( {T_{meas13\_ y11} - T_{meas13\_ y22}} \right)^{2}} + T_{meas13\_ y22}} \right)}{2T_{meas13\_ y21}}} & (21)\end{matrix}$

[0121] and $\begin{matrix}{\frac{{Ty}_{22}}{{Ty}_{21}} = \frac{\left( {{- T_{meas13\_ y11}} + \sqrt{{4T_{meas13\_ y12}T_{meas13\_ y21}} + \left( {T_{meas13\_ y11} - T_{meas13\_ y22}} \right)^{2}} + T_{meas13\_ y22}} \right)}{2T_{meas13\_ y21}}} & (22)\end{matrix}$

[0122] From equation (19), $\quad\begin{matrix}\frac{{Ty}_{12}}{{Ty}_{11}} & {and} & \frac{{Ty}_{22}}{{Ty}_{21}}\end{matrix}$

[0123] in terms of the corresponding the S-parameters for the erroradapter Y is also given by: $\begin{matrix}{\frac{{Ty}_{12}}{{Ty}_{11}} = {{- {Sy}_{11}} = D}} & (23)\end{matrix}$

[0124] and $\begin{matrix}{\frac{{Ty}_{22}}{{Ty}_{21}} = {{\frac{{Sy}_{12}{Sy}_{21}}{{Sy}_{22}} - {Sy}_{11}} = C}} & (24)\end{matrix}$

[0125] As one of ordinary skill in the art can appreciate, equations(21) and (22) are equal and because of the square root have twosolutions. The smaller value or the first solution, defined by Sy₁₁,corresponds to the directivity error of the Y error adapter. The largervalue or the second solution, defined by C, corresponds to the errorcoefficient, ${\frac{{Sy}_{12}{Sy}_{21}}{{Sy}_{22}} - {Sy}_{11}},$

[0126] for the Y error adapter.

[0127] With reference to the portion of the calibration procedure thatmeasures the high reflect calibration standard as illustrated in FIGS. 3and 4 of the drawings, the high reflect standard 301, is connected toone measurement port 103 ₁ of the first direct pair and the same highreflect standard 301 is disconnected from the measurement port 103 ₁ andis then connected to the other measurement port 103 ₃ of the directpair. With specific reference to FIG. 19 of the drawings the followingequation can be written: $\begin{matrix}{\Gamma_{{meas\_ reflect}{\_ x}} = {{Sx}_{11} + \frac{{Sx}_{12}{Sx}_{21}\Gamma_{{act\_ reflect}{\_ x}}}{1 - {{Sx}_{22}\Gamma_{{act\_ reflect}{\_ x}}}}}} & (25)\end{matrix}$

[0128] where Γ_(meas) _(—) _(reflect) _(—) _(x) is the measuredreflection coefficient of the high reflect standard 301 at themeasurement port capable of connection to the first test channel,measurement port 103 ₁ in the first direct pair, and Γ_(act) _(—)_(reflect) _(—) _(x) is the actual reflection coefficient of the highreflect standard at the same measurement port 103 ₁. The same highreflect calibration standard 301 is connected to the opposite port inthe first direct pair, measurement port 103 ₃ in the specific example.With respect to the error adapter Y, the following equation can also bewritten: $\begin{matrix}{\Gamma_{{meas\_ reflect}{\_ y}} = {{Sy}_{11} + \frac{{Sy}_{12}{Sy}_{21}\Gamma_{{act\_ reflect}{\_ y}}}{1 - {{Sy}_{22}\Gamma_{{act\_ reflect}{\_ y}}}}}} & (26)\end{matrix}$

[0129] where Γ_(meas) _(—) _(reflect) _(—) _(y) is the measuredreflection coefficient of the high reflect standard 301 at measurementport 103 ₃ and Γ_(act) _(—) _(reflect) _(—) _(y) is the actualreflection coefficient of the high reflect standard at the measurementport 103 ₃. A value for the measured reflection coefficient of the highreflect standard, Γ_(meas) _(—) _(reflect) _(—) _(x), for themeasurement port 103 ₁ may be obtained from the following measured andstored arrays A_(reflect) _(—) ₁/R1_(reflect) _(—) ₁. Similarly, a valuefor the measured reflection coefficient of the high reflect standard,Γ_(meas) _(—) _(reflect) _(—) _(y), for the measurement port 103 ₃ maybe obtained from the following measured and stored arrays B_(reflect)_(—) ₃/R2_(reflect) _(—) ₃. Because the same high reflect standard isconnected to measurement ports 103 ₁ and 103 ₃, it is possible to solvefor Γ_(act) _(—) _(reflect) _(—) _(x) in equation (25) and Γ_(act) _(—)_(reflect) _(—) _(y) in equation (26), and set the r terms equal to eachother. From the resulting relationship and equations (13), (14), (23),(24), (25) and (26), the following relationship can be written:$\begin{matrix}{{Sx}_{22} = \frac{\left( {B - \Gamma_{{meas\_ reflect}{\_ x}}} \right)\left( {C - \Gamma_{{meas\_ reflect}{\_ y}}} \right){Sy}_{22}}{\left( {A - \Gamma_{{meas\_ reflect}{\_ x}}} \right)\left( {D - \Gamma_{{meas\_ reflect}{\_ y}}} \right)}} & (27)\end{matrix}$

[0130] As one of ordinary skill in the art appreciates, equation (27)has two unknown terms, but permits the expression of Sx₂₂ in terms ofSy₂₂. Accordingly, another relationship is necessary in order to solvefor these two unknown terms.

[0131] With specific reference to FIGS. 7 and 19, the following equationcan also be written: $\begin{matrix}{\Gamma_{meas\_ thru11} = {{Sx}_{11} + \frac{{Sx}_{12}{Sx}_{21}{Sy}_{22}}{1 - {{Sx}_{22}{Sy}_{22}}}}} & (28)\end{matrix}$

[0132] where Γ_(meas) _(—) _(thru11) is measured as A_(f13) _(—)_(thru)/R1_(f13) _(—) _(thru) for the measurement port of the firstdirect pair that is capable of connection to the first test channel 111.From (13), (14), (23) and (24), the following can be written$\begin{matrix}{{Sx}_{22} = \sqrt{\frac{\left( {B - \Gamma_{{meas\_ reflect}{\_ x}}} \right)\left( {C - \Gamma_{{meas\_ reflect}{\_ y}}} \right)\left( {B - \Gamma_{meas\_ thru11}} \right)}{\left( {A - \Gamma_{{meas\_ reflect}{\_ x}}} \right)\left( {D - \Gamma_{{meas\_ reflect}{\_ y}}} \right)\left( {A - \Gamma_{meas\_ thru11}} \right)}}} & (29)\end{matrix}$

[0133] and Sx_(22 may) be calculated. Sx₂₂ is the source match errorcoefficient at the first measurement port 103 ₁. Due to the square rootin equation (29), there are 2 solutions for Sx₂₂. Having an approximatevalue of the argument of the high reflect calibration standard, however,the correct choice can be made. For example a short circuit calibrationstandard should have an argument of 180 degrees and an open circuitcalibration standard should have an argument of zero degrees. If anon-zero thru 601 is used, then the phase rotation of the reflect 301 iscalculated from the electrical length of the non-zero through. From thiscalculation, a correct solution for Sx₂₂ from equation (29) is apparent.Accordingly, the type of reflect 301, whether a short circuit or an opencircuit, and an electrical length of the non-zero thru must be known. Ifthe reflect 301 is an offset short, it is also necessary to know thephase of the offset.

[0134] When a value for Sx₂₂ is known, a value for Sy₂₂ may becalculated from equation (27). Sy₂₂ is the source match errorcoefficient of error adapter Y at the measurement port capable ofconnection to the second test channel 112, which is measurement port 103₃ in the specific example.

[0135] Because a definite value for Sx₂₂ is known, equations (13), (14)and (29) permit calculation of a reflection tracking coefficient for theerror adapter X and is given by:

Sx ₁₂ Sx ₂₁=(B−A)Sx ₂₂   (30)

[0136] Similarly, a definite value for Sy₂₂ and equations (23), (24) and(27) permit calculation of a reflection tracking for the error adapter Yand is given by:

Sy ₁₂ Sy ₂₁=(D−C)SY ₂₂   (31)

[0137] At this point in the process, the directivity, source match andreflection tracking for the error adapter X and the error adapter Y aredetermined. The X error adapters are defined as the error artifactspresented in series with the measurement ports 103 capable of connectionto the first test channel 111. Similarly, the Y error adapters aredefined as the error artifacts presented in series with the measurementports 103 capable of connection to the second test channel 112.

[0138] In the specific four-port embodiment, the measurements andcalculations described herein for measurement ports 103 ₁ and 103 ₃yield directivity, source match and reflection tracking for the erroradapter X related to measurement port 103 ₁ and directivity, sourcematch, and reflection tracking for the error adapter Y related tomeasurement port 103 ₃. The same measurements and calculations describedherein for measurement ports 103 ₁ and 103 ₃ are performed for thesecond direct pair. Specifically, measurements and calculations are madefor measurement ports 103 ₂ and 103 ₄ to yield directivity, source matchand reflection tracking for the error adapter X related to measurementport 103 ₂ and directivity, source match, and reflection tracking forthe error adapter Y related to measurement port 103 ₄. In a multiportembodiment, the same measurements and calculations are made for eachdirect pair to yield directivity, source match and reflection trackingfor the error adapter X related to the measurement port of the directpair capable of connection to the first test channel 111 anddirectivity, source match, and reflection tracking for the error adapterY related to the measurement port of the direct pair capable ofconnection to the second test channel 112. Accordingly, a 2N port DUT100 has N different X error adapter and N different Y error adapterassociated therewith.

[0139] Using the forward reflection and transmission measurements madeon the terminated thru 601, which in a specific example of the firstdirect pair are the A_(f13) _(—) _(termthru)/R1_(f13) _(—) _(termthru)and B_(f13) _(—) _(termthru)/R1_(f13) _(—) _(termthru) arrays, it ispossible to solve for a load match error coefficient presented at themeasurement port capable of connection to the second test channel 112and a forward transmission tracking error coefficient for the firstdirect pair. The load match for the measurement port 103 ₃,Γ_(L3), andforward transmission tracking for the first direct pair,τ₁₃, are givenby: $\begin{matrix}{\Gamma_{L3} = \frac{{Sx}_{11} - \left( {A_{f13\_ termthru}/{R1}_{f13\_ termthru}} \right)}{{{Sx}_{11}{Sx}_{22}} - {{Sx}_{12}{Sx}_{21}} - {{Sx}_{22}\left( {A_{f13\_ termthru}/{R1}_{f13\_ termthru}} \right)}}} & (32)\end{matrix}$

[0140] and

τ₁₃=(B _(f13) _(—) _(termthru) /R1_(f13) _(—) _(termthru))(1−SX₂₂Γ_(L3))   (33)

[0141] Using the reverse reflection and transmission measurements madeon the terminated thru 601, which in a specific example of the firstdirect pair are the A_(r13) _(—) _(termthru)/R2_(r13) _(—) _(termthru)and B_(r13) _(—) _(termthru)/R2_(f13) _(—) _(termthru) arrays, it ispossible to solve for a load match error coefficient presented at themeasurement port capable of connection to the first test channel 111 anda reverse transmission tracking error coefficient for the first directpair. The load match for the measurement port 103 ₁,Γ_(L1), and thereverse transmission tracking coefficient,τ₃₁, are given by:$\begin{matrix}{\Gamma_{L1} = \frac{{Sy}_{11} - \left( {B_{r13\_ termthru}/{R2}_{r13\_ termthru}} \right)}{{{Sy}_{11}{Sy}_{22}} - {{Sy}_{12}{Sy}_{21}} - {{Sy}_{22}\left( {B_{r13\_ termthru}/{R2}_{r13\_ termthru}} \right)}}} & (34)\end{matrix}$

[0142] and

τ₃₁₌₍ A _(r13) _(—) _(termthru) /R2_(r13) _(—) _(termthru))(1−SY₂₂Γ_(L1))   (35)

[0143] In the specific illustrated embodiment, using the measurementsmade of the terminated thru for the second direct pair, the samealgorithmic formulations shown in equations (32) through (35) asdescribed for measurement ports 103 ₁ and 103 ₃ are applied to themeasurement ports 103 ₂ and 103 ₄. Accordingly, directivity, sourcematch, reflection tracking and load match error coefficients for eachmeasurement port in the first and second direct pairs and forward andreverse transmission tracking error coefficients for the first andsecond direct pairs are determined. In a multiport embodiment of amethod according to the teachings of the present invention, thedirectivity, source match, reflection tracking and load match errorcoefficients for each measurement port in all of the direct pairs andforward and reverse transmission tracking error coefficients for all ofthe direct pairs are similarly determined.

[0144] Using the measurements of the thru 601 using the first indirectpair, measurement ports 103 ₁ and 103 ₄, the forward and reversetransmission tracking error coefficients,τ₁₄ and τ₄₁, is determined. Themeasured and stored arrays, A_(f14) _(—) _(thruterm)/R1_(f14) _(—)_(thru) _(—) _(term and B) _(f14) _(—) _(thruterm)/R1_(f14) _(—)_(thruterm), are inserted into an equation similar to equation (33) andthe measured and stored arrays, A_(r14) _(—) _(thruterm)/R2_(r14) _(—)_(thru) _(—) _(term) and B_(r14) _(—) _(thruterm)/R2_(r14) _(—)_(thruterm), are inserted in an equation similar to equation (35). Usingthe load match error coefficients already calculated for each of themeasurement ports 103, the forward and reverse transmission tracking forthe indirect pair comprising measurement ports 103 ₁ and 103 ₄ iscalculated as follows:

τ₁₄=(B _(f14) _(—) _(termthru) /R1_(f14) _(—) _(termthru))(1−SX₂₂Γ_(L4))   (36)

[0145] and

τ₄₁=(A _(r4l) _(—) _(termthru) /R2_(r41) _(—) _(termthru))(1−SX₂₂Γ_(L1))   (37)

[0146] Similar calculations are made for the remaining indirect pairs.In the specific embodiment illustrated, the measured and stored arrays,A_(f23) _(—) _(thruterm)/R1_(f23) _(—) _(thru) _(—) _(term) and B_(f23)_(—) _(thruterm)/R1_(f23) _(—) _(thruterm), are used to calculate theforward transmission tracking error coefficient for the indirect paircomprising measurement ports 103 ₂ and 103 ₃ and the measured and storedarrays, A_(r23) _(—) _(thruterm)/R2_(r23) _(—) _(thruterm) and B_(r23)_(—) _(thruterm)/R2_(r23) _(—) _(thruterm), are used to calculate thereverse transmission tracking error coefficient for the same indirectpair.

[0147] Forward and reverse transmission tracking error coefficientsbetween the measurement ports 103 capable of connection to the same testchannel, either the first test channel 111 or the second test channel112, are herein referred to as “proximal pairs”. In the specificillustrated embodiment the proximal pairs are measurement ports 103 ₁and 103 ₂, measurement ports 103 ₃ and 103 ₄. The related forward andreverse transmission tracking error coefficients of the proximal pairsare; τ₁₂, τ₂₁, τ₃₄, and τ₄₃, which may be determined either throughmeasurement and calculation or through pure calculation. The method forpure calculation of the forward and reverse transmission tracking errorcoefficients is taught in the '040 patent application Ser. No.

[0148] The forward transmission tracking error coefficient for eachproximal pair where both measurement ports 103 of the proximal pair arecapable of connection to the first test channel 111 is measured andcalculated by connecting the thru 601 between the measurement ports 103of the proximal pair, connecting the signal generator 105 to a first oneof the measurement ports 103 of the proximal pair and terminating thesampling arm 113 in a local terminating impedance 116. For purposes ofnomenclature, the first measurement port 103 of the proximal pair isdesignated as “port F”. The other measurement port 103 of the proximalpair, which for purposes of nomenclature is designated as “port G”, isterminated in a local terminating impedance 104, and the respectivesampling arm 113 is connected to the first test channel 111. The VNA 200measures and stores a ratio of a transmission response over thereference signal, A_(fFG) _(—) _(termthru)/R1_(fFG) _(—) _(termthru).The ratio is used in the transmission tracking error coefficientequation where:

τ_(FG)=(A _(fFG) _(—) _(termthru) /R1_(fFG) _(—) _(termthru))(1Sx ₂₂_(—) _(portF)Γ_(portF))   (38)

[0149] The reverse transmission tracking error coefficient for the sameproximal pair, ports F&G, where both measurement ports 103 of theproximal pair are capable of connection to the first test channel 111 ismeasured and calculated by keeping the connection of the thru 601between the measurement ports 103 of the proximal pair, connecting thesignal generator 105 to the second one of the measurement ports 103 ofthe proximal pair and terminating the sampling arm 113 in a localterminating impedance 116. The first one of the measurement ports 103 ofthe proximal pair is terminated in the local terminating impedance 104,and the respective sampling arm 113 is connected to the first testchannel 111. The VNA 200 measures and stores a ratio of a transmissionresponse over the reference signal, A_(rFG) _(—) _(termthru)/R1_(rFG)_(—) _(termthru). The ratio is used in the transmission tracking errorcoefficient equation where:

τ=(A _(rFG) _(—) _(termthru) /R1_(rFG) _(—) _(termthru))(1−Sx ₂₂ _(—)_(portG)Γ_(portG))   (39)

[0150] For purposes of illustration and with specific reference to FIG.20, there is shown connection diagrams for the determination of theforward and reverse transmission tracking error coefficients for theproximal pair comprising measurement ports 103 ₁ and 103 ₂. The forwardtransmission measurement is made by connecting the signal generator 105to the first signal path 107. The switch network 150 is configured sothat the first signal path 107 is connected to the measurement port 103₁ and the respective sampling arm 113 ₁ is terminated in the localsampling arm impedance 116 ₁. The switch network 150 is furtherconfigured so that the measurement port 103 ₂ is terminated in the localterminating impedance 104 ₂ and the sampling arm 113 ₂ is connected tothe first test channel 111. The signal generator 105 sweeps through theplurality of frequencies that define the desired frequency range andmeasures the ratio A_(f12) _(—) _(termthru)/R1_(f12) _(—) _(termthru).Using equation (37) the forward transmission tracking error coefficientfor the proximal pair is calculated as:

Γ₁₂=(A _(f12) _(—) _(termthru) /R1_(f12) _(—) _(termthru))(1−SX ₂₂ _(—)_(port1)Γ_(port1))

[0151] The thru 601 connection and the signal transfer switch 106configuration are maintained. With specific reference to FIG. 21 of thedrawings, the switch network 150 is reconfigured so that the measurementport 103 ₂ is connected to the first signal path 107 and the respectivesampling arm 113 ₂ is terminated in the local sampling terminatingimpedance 116 ₂. Additionally, the switch network 150 is configured sothat the measurement port 103 ₁ is terminated in the local terminatingimpedance 104 ₁ and the sampling arm 113 ₁ is connected to the firsttest channel 111. The signal generator 105 sweeps through the pluralityof frequencies that define the desired frequency range and measures theratio A_(r12) _(—) _(termthru)/R1_(r12) _(—) _(termthru). Using equation(38) the reverse transmission tracking error coefficient for theproximal pair is calculated as:

τ₂₁=(A _(r12) _(—) _(termthru) /R1_(r12) _(—) _(termthru))(1−SX ₂₂ _(—)_(port2)Γ_(port2))

[0152] The same measurement and calculation process is repeated for theremaining proximal pairs, which in the illustrated embodiment is theproximal pair comprising measurement ports 103 ₃ and 103 ₄. As one ofordinary skill in the art appreciates, the measurements for the proximalpair capable of connection to the second test channel 112 are carriedout using the same process, but with the second test channel 112 and thesecond reference channel 202 as measurement devices. In a multiportembodiment, the measurement and calculation process is repeated for allof the proximal pairs.

[0153] With specific reference to FIGS. 22 through 26 of the drawings,there is shown a flow chart of a method according to the teachings ofthe present invention in which a reflect standard 301 is connected 2201to one port of a first direct pair and the switch network 150 isconfigured for measurement 2202 by the VNA 200 of a ratio of thereflection response over the stimulus. See FIG. 3 of the drawings. Theratio yields a value for a number of frequencies in a desired frequencyrange. The numbers are stored in a data array where each element of thedata array holds the measured ratio at a single frequency. The reflect301 is then disconnected and reconnected 2203 to the other port in thedirect pair, the switch network 150 is reconfigured, and the other portin the direct pair is stimulated and the ratio of the reflectionresponse over the stimulus is measured and stored 2204 in another dataarray. See FIG. 4 of the drawings. In a preferred embodiment, thedesired frequency range for which all measurements are taken is thesame. In this case, each element in the data arrays represents measuredresults at the same frequency point along the desired frequency range.

[0154] The flow chart continues with step of connecting 2301 andconfiguring 2302 the switch network 150 for measurement of the line 401between ports of the same direct pair. The VNA 200 measures 2302 aforward direction reflection and transmission response at themeasurement ports 103 of the direct pair at the first and second testchannels 111, 112 as well as the first and second reference channels201, 202. The switch network 150 is then reconfigured 2303 for thereverse direction measurement and the VNA 200 then measures 2303 areverse direction reflection and transmission response at themeasurement ports 103 of the direct pair at the first and second testchannels 111, 112 as well as the first and second reference channels201, 202. Not shown in the flow chart is the connection and measurementof the matched loads 501 as shown in FIG. 6 of the drawings to extendthe calibration to the lower frequency range.

[0155] With specific reference to FIGS. 23, 7, and 8 of the drawings,the flow chart continues with the step of connecting 2401 the thru 601to the measurement ports 103 of the same direct pair. The switch network150 is configured 2402 for forward direction measurement of the thru601, and the forward direction reflection and transmission responses andthe reference channel signals are measured and stored in data arrays.The switch network 150 is then reconfigured 2403 for the reversedirection measurements and the reverse direction reflection andtransmission responses and the reference channel signals are measuredand stored in data arrays.

[0156] With specific reference to FIGS. 23 and 9 of the drawings, thethru 601 remains connected and the switch network 150 is reconfigured2501 for a forward direction measurement, where the thru 601 is locallyterminated in a local impedance 104 within the switch network 150. Theforward direction reflection and transmission responses of the locallyterminated thru 601 are measured and stored as well as the referencechannel signals. The switch network 150 is then reconfigured 2502 for areverse direction measurement of the locally terminated thru 601, thereverse reflection and transmission responses and the reference channelsignals are measured and stored. The process repeats 2503 for all directpairs of measurement ports. The indices n and m as shown in the flowchart represent that the process increments through all of the directpairs. As one of ordinary skill in the art appreciates, the direct pairsmay be defined in another way than is illustrated herein in which case,the step of incrementing through the direct pairs as shown by referencenumeral 2504 uses a different convention. After incrementing to the nextdirect pair, the process steps repeat (See connector E in FIG. 22 of thedrawings) until all direct pairs are measured. See FIGS. 10 through 16for an illustrative representation of the measurements made on thesecond direct pair.

[0157] With specific reference to FIGS. 24 and 19 of the drawings, thedirectivity 1901, source match 1902 and reflection tracking 1903 errorcoefficients for the X error adapter 1910 are calculated 2601 from thestored data arrays. The directivity 1904, source match 1905 andreflection tracking 1906 error coefficients for the Y error adapter 1920are also calculated 2602 from the stored data arrays. Using the resultsof the calculations, the load match and transmission tracking errorcoefficients are then calculated for both the X and Y error adapters.The calculation process is repeated 2604 for all direct pairs.

[0158] With specific reference to FIGS. 24, 17, and 18, the thru 601 isconnected 2701 between the measurement ports 103 of the first indirectpair. The switch network 150 is configured 2702 for a forward directionmeasurement with the thru 601 locally terminated in the switch network150. The forward reflection and transmission responses and the first andsecond reference channels are measured. The measured results are storedin additional data arrays. The switch network 150 is reconfigured 2703for a reverse direction measurement with the thru 601 locally terminatedin the switch network 150. The reverse reflection and transmissionresponses and the first and second reference channels are measured. Themeasured results are stored in data arrays. This process is repeated2704 for all indirect pairs. As one of ordinary skill in the artappreciates, the indirect pairs may be defined in many different ways.The flow chart illustrates one method where the measurement port 103capable of connection to the first test channel 111 is incremented from1 to N−1 and while the measurement port 103 capable of connection to thesecond test channel 112 is incremented from N+2 to 2N. The last indirectpair is between measurement ports 103 N and N+1. Other methods dependingupon the definition of the measurement ports 103 that make up theindirect pairs differ from the one illustrated herein.

[0159] With specific reference to FIG. 25 of the drawings, the flowchart continues with the steps of calculating 2801 a transmissiontracking coefficient for each indirect pair. The process increments 2802through all of the indirect pairs in the same way as for the measurementportion of the indirect pairs.

[0160] With specific reference to FIGS. 25, 20, and 21, the process thencontinues with the steps of connecting the thru 601 between themeasurement ports 103 that comprise proximal pairs. In the illustratedembodiment, the proximal pairs are the measurement ports 103 that areadjacent to each other. The thru 601 is connected 2803 between a firstproximal pair as shown in FIG. 20 and the switch network 150 isconfigured 2804 for a forward direction measurement of the thru 601 in alocally terminated condition. See FIG. 20 of the drawings. A ratio ofthe forward transmission response over the stimulus as measured by thefirst reference channel is measured and stored 2804 in a data array. Theswitch network 150 is reconfigured 2805 for a reverse directionmeasurement. See FIG. 21 of the drawings. A ratio of the reversetransmission response over the stimulus as measured by the firstreference channel is measured and stored 2805 in a data array. The stepsfor the proximal pairs are repeated 2806 for each proximal pair. As oneof ordinary skill in the art appreciates, the method of incrementing themeasurement ports 103 in the loop 2806 for repetition of the process foreach proximal pair begins with measurement ports 103 _(n) and 103 _(m)where n=1 and m=n+1. Both n and m are incremented through the process,although there is one condition where n and m actually define anindirect pair. In that case, the process steps are not performed.

[0161] With specific reference to FIG. 26 of the drawings, the flowchart continues with the steps of calculating 2901 the transmissiontracking error coefficients for each one of the proximal pairs.

[0162] When all of the systematic error coefficients are determined, theDUT 101 is inserted for measurement 2902. The measured DUT data is thencorrected 2903 according to the teachings of the '040 patent applicationSer. No. by using all of the systematic error coefficients calculated astaught herein. Advantageously, a method and apparatus according to theteachings herein provides an improved characterization of the errorartifacts present in measurements made of the DUT 101 with the VNA 200.This provides for a more accurate characterization of the frequencyresponse of the DUT 101 as distinct from the frequency responsecontributions of the error artifacts that are part of the measurementsystem.

1. A method of calibrating a measurement path comprising the steps of:providing a vector network analyzer having at least two referencereceivers, and a total of 2N measurement ports, wherein N is an integer,presenting a high reflect calibration standard and measuring areflection characteristic for each said measurement port, presenting aline calibration standard between N direct pairs of said measurementports and measuring forward and reverse reflection and transmissioncharacteristics for each one of said N direct pairs of said measurementports, presenting a through calibration standard between said N directpairs of said measurement ports and measuring forward and reversereflection and transmission characteristics for each one of said N pairsof said measurement ports, and calculating directivity, source match,and reflection tracking error coefficients for each one of saidmeasurement ports.
 2. A method of calibrating as recited in claim 1 andfurther comprising the steps of presenting said through calibrationstandard between N−1 indirect pairs of said measurement ports, measuringforward and reverse reflection and transmission characteristics, andcalculating a load match error coefficient for each measurement port. 3.A method of calibrating as recited in claim 2 and further comprising thesteps of calculating forward transmission tracking and reversetransmission tracking error coefficients for each one of said N directpairs and N−1 indirect pairs of said measurement ports.
 4. A method ofcalibrating as recited in claim 3 and further comprising the steps of:connecting said through calibration standard between proximal pairs ofsaid measurement ports, measuring reflection and transmission responsesof said proximal pairs when said through calibration standard isconnected therebetween, and calculating forward and reverse transmissiontracking error coefficients for each one of said proximal pairs.
 5. Amethod of measuring comprising the method of calibrating as recited inclaim 3 and further comprising the steps of measuring a 2N port device,and correcting a result of said step of measuring using saiddirectivity, source match, reflection tracking, load match, forwardtransmission tracking, and reverse transmission tracking errorcoefficients.
 6. A method of calibrating as recited in claim 1 whereinsaid high reflect standard is a short circuit.
 7. A method ofcalibrating as recited in claim 1 wherein said high reflect standard isan open circuit.
 8. A method of calibrating as recited in claim 1wherein said line calibration standard is a first calibration standardhaving a first frequency range and further comprising the steps ofpresenting to each measurement port of said N direct pairs of saidmeasurement ports a second calibration standard having a secondfrequency range and measuring forward and reverse reflection andtransmission characteristics for each one of said N direction pairs ofsaid measurement ports thereby extending a frequency range of saidcalibration method.
 9. A method of calibrating as recited in claim 1 andfurther comprising the steps of presenting to each measurement port ofsaid N direct pairs of said measurement ports two matched loads andmeasuring forward and reverse reflection and transmissioncharacteristics for each one of said N direction pairs of saidmeasurement ports thereby extending a frequency range of saidcalibration method to lower frequencies.
 10. A method of calibrating asrecited in claim 1 and further comprising the step of correcting saidforward and reverse reflection and transmission characteristics fromsaid step of measuring said line calibration standard and said step ofmeasuring said through calibration standard for said N direct pairs ofsaid measurement ports for effects of a transfer switch before saidsteps of calculating directivity, source match, and reflection trackingfor each one of said measurement ports.
 11. A method of calibrating asrecited in claim 10 wherein said step of correcting uses theformulation: $S_{corrected} = \begin{bmatrix}\left\{ \frac{\frac{A_{f}}{{R1}_{f}} - {\frac{A_{r}}{{R2}_{r}}\frac{{R2}_{f}}{{R1}_{f}}}}{1 - {\frac{{R2}_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}} \right\} & \left\{ \frac{\frac{A_{r}}{{R2}_{r}} - {\frac{A_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}}{1 - {\frac{{R2}_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}} \right\} \\\left\{ \frac{\frac{B_{f}}{{R1}_{f}} - {\frac{B_{r}}{{R2}_{r}}\frac{{R2}_{f}}{{R1}_{f}}}}{1 - {\frac{{R2}_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}} \right\} & \left\{ \frac{\frac{B_{r}}{{R2}_{r}} - {\frac{B_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}}{1 - {\frac{{R2}_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}} \right\}\end{bmatrix}$

where A_(f), A_(r), B_(f), B_(r), R1_(f), R1, R2_(f), R2_(r) aremeasurements taken by a first test channel in a forward direction, saidfirst test channel in a reverse direction, a second test channel in aforward direction, said second test channel in a reverse direction, afirst reference channel in a forward direction, said first referencechannel in a reverse direction, a second reference channel in a forwarddirection, and said second reference channel in a reverse direction,respectively.
 12. An apparatus for calibrating a measurement pathcomprising: a vector network analyzer having at least two referencereceivers, two test channels, and a total of 2N measurement ports,wherein N is an integer, means for measuring and storing high reflectcharacteristics for each said measurement port when a high reflectcalibration standard is connected thereto, line forward and reversereflection and transmission characteristics for each one of N directpairs of said measurement ports when a line calibration standard isconnected therebetween, direct through forward and reverse reflectionand transmission characteristics for each one of said N direct pairs ofsaid measurement ports when a through calibration standard is connectedtherebetween, and indirect through forward and reverse reflection andtransmission characteristics for each one of said N−1 indirect pairs ofsaid measurement ports when said through calibration standard isconnected therebetween, means for calculating directivity, source match,reflection tracking for each one of said direct pairs of saidmeasurement ports.
 13. An apparatus for calibrating as recited in claim12 and further comprising means for measuring forward and reversereflection and transmission characteristics, and calculating a loadmatch error coefficient for each measurement port.
 14. An apparatus forcalibrating as recited in claim 13 and further comprising means forcalculating forward transmission tracking and reverse transmissiontracking for each one of said N direct pairs and N−1 indirect pairs ofsaid measurement ports.
 15. An apparatus for calibrating as recited inclaim 13 wherein said means for measuring further comprises a means formeasuring reflection and transmission responses of proximal pairs ofsaid measurement ports when a through calibration standard is connectiontherebetween and said means for calculating further comprises a meansfor calculating forward and reverse transmission tracking errorcoefficients for each one of said proximal pairs.
 16. An apparatus formeasuring comprising the apparatus for calibrating as recited in claim14 and wherein said means for measuring further comprises means formeasuring a 2N port device to obtain DUT measurements, and saidapparatus further comprises a means for correcting said DUT measurementsusing said directivity, source match, reflection tracking, load match,forward transmission tracking, and reverse transmission tracking errorcoefficients.
 17. An apparatus for calibrating as recited in claim 12and further comprising means for measuring a 2N port device resulting ina raw measurement of said 2N port device and a means for correcting saidraw measurement using said directivity, source match, reflectiontracking, load match, forward transmission tracking, and reversetransmission tracking values.
 18. An apparatus for calibrating asrecited in claim 12 said high reflect standard further comprising ashort circuit calibration standard.
 19. An apparatus for calibrating asrecited in claim 12 said high reflect standard further comprising anopen circuit calibration standard.
 20. An apparatus for calibrating asrecited in claim 12 wherein said line calibration standard is a firstcalibration standard having a first frequency range and furthercomprising the steps of presenting to each measurement port of said Ndirect pairs of said measurement ports a second calibration standardhaving a second frequency range and measuring forward and reversereflection and transmission characteristics for each one of said Ndirection pairs of said measurement ports thereby extending a frequencyrange of said calibration method.
 21. An apparatus for calibrating asrecited in claim 12 said means for measuring and storing furthercomprising means for measuring and storing matched load forward andreverse reflection and transmission characteristics for each one of saidN direct pairs of said measurement ports thereby extending a frequencyrange of said calibration method to lower frequencies.
 22. An apparatusfor calibrating as recited in claim 12, wherein said step of measuringand storing results in raw line forward and reverse reflection andtransmission characteristics and raw through forward and reversereflection and transmission characteristics and further comprising meansfor correcting said raw line forward and reverse reflection andtransmission characteristics and said raw through forward and reversereflection and transmission characteristics for said N direct pairs ofsaid measurement ports for effects of a transfer switch.
 23. Anapparatus for calibrating as recited in claim 22 wherein said step ofcorrecting uses the formulation: $S_{corrected} = \begin{bmatrix}\left\{ \frac{\frac{A_{f}}{{R1}_{f}} - {\frac{A_{r}}{{R2}_{r}}\frac{{R2}_{f}}{{R1}_{f}}}}{1 - {\frac{{R2}_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}} \right\} & \left\{ \frac{\frac{A_{r}}{{R2}_{r}} - {\frac{A_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}}{1 - {\frac{{R2}_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}} \right\} \\\left\{ \frac{\frac{B_{f}}{{R1}_{f}} - {\frac{B_{r}}{{R2}_{r}}\frac{{R2}_{f}}{{R1}_{f}}}}{1 - {\frac{{R2}_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}} \right\} & \left\{ \frac{\frac{B_{r}}{{R2}_{r}} - {\frac{B_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}}{1 - {\frac{{R2}_{f}}{{R1}_{f}}\frac{{R1}_{r}}{{R2}_{r}}}} \right\}\end{bmatrix}$

where A_(f), A_(r),B_(f),B_(r),R1_(f),R1_(r),R2_(f),R2_(r) aremeasurements taken by a first test channel in a forward direction, saidfirst test channel in a reverse direction, a second test channel in aforward direction, said second test channel in a reverse direction, afirst reference channel in a forward direction, said first referencechannel in a reverse direction, a second reference channel in a forwarddirection, and said second reference channel in a reverse direction,respectively.